The $h$–principle for broken Lefschetz fibrations
The $h$–principle for broken Lefschetz fibrations
复制标题
Lefschetz 纤维断裂的 $h$– 原理
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Jonathan D. Williams
中科院分区：
文献类型：
--
作者：
Jonathan D. Williams
众所周知，任意光滑、定向的4-流形允许存在所谓的破碎Lefschetz纤维的结构。给定一个断裂的纤维，有一些特定的修改，实现为纤维映射的同伦，使人们能够构造同一流形的无限多个不同的纤维。本文的目的是证明这些修正足以获得给定同伦类光滑映射中的每一个断纤维。一个值得注意的应用是，增加一个额外的“投影”移动会生成所有破碎的纤毛，而不考虑同伦类别。文章最后指出了进一步的应用和有待解决的问题。
It is known that an arbitrary smooth, oriented 4-manifold admits the structure of what is called a broken Lefschetz fibration. Given a broken fibration, there are certain modifications, realized as homotopies of the fibration map, that enable one to construct infinitely many distinct fibrations of the same manifold. The aim of this paper is to prove that these modifications are sufficient to obtain every broken fibration in a given homotopy class of smooth maps. One notable application is that adding an additional "projection" move generates all broken fibrations, regardless of homotopy class. The paper ends with further applications and open problems.